find the exact value of sin 15 degrees
Answer:
Hi,
Step-by-step explanation:
sin(a-b)=sin(a) cos(b)+ cos(a) sin(b)
a=45° and b=30°
[tex]sin(45^o-30^o)=sin(45^o)*cos(30^o)+cos(45^o)*sin(30^o)\\\\=\dfrac{\sqrt{2}}{2}* \dfrac{\sqrt{3}}{2}+\dfrac{\sqrt{2}}{2}*\dfrac{1}{2}\\\\\\\boxed{sin(15^o)=\dfrac{\sqrt{2}}{4}*(1+\sqrt{3} )}\\[/tex]
how many terms are in 10y2-3y+8
Hi student, let me help you out! :)
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We are asked to find how many terms are in [tex]\pmb{10y^2-3y+8}[/tex].
[tex]\triangle~\fbox{\bf{KEY:}}[/tex]
A term is a thing that's added or subtracted.So let's compute the number of terms in this expression.
The first term is [tex]\pmb{10y^2}[/tex].
Is anything added or subtracted from 10y²?
Sure! [tex]\pmb{-3y}[/tex] is subtracted from 10y².
Also, 8 is added to -3y.
Thus, this expression has 3 terms.
Hope it helps you out! :D
Ask in comments if any queries arise.
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~Just a smiley person helping fellow students :)
What is one third divided by eight
Answer:
[tex]\frac{1}{24}[/tex]
Step-by-step explanation:
(1/3)/(8/1)
cross multiply
(1*1=1)/(3*8=24)
1/24
Answer:
= 1/24
One third divided by eight is 1/24.
Step-by-step explanation:
first we make an equation then simplfy it further
⇒1/3 ÷ 8
convert the division sign into multiplication by using the mutiplicative inverse of 8
⇒1/3 × 1/8
multiply the numerators together and denominators together
⇒1/24 ...answer...
hope that helps...
solve 2(r+6) =(6+1/3r)
Answer:
r = - 18/5
I hope this helps! ^^
( This problem has 13 steps, so it would take a lot of time to type them in ^^)
A person invests 1000 dollars in a bank. The bank pays 6.75% interest compounded monthly. To the nearest tenth of a year, how long must the person leave the money in the bank until it reaches 2500 dollars?
Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. The time for which the person must leave the money in the bank until it reaches $2500 is 1.2.
What is compound interest?Interest on interest, or compound interest, is the adding of interest to the principal sum of a loan or deposit. It's the outcome of reinvesting interest rather than paying it out so that interest is received on the principal plus previously collected interest in the next quarter.,
[tex]A = P(1+ \dfrac{r}{n})^{nt}[/tex]
where A is the final amount
P is the principal amount
r is the rate of interest
n is the number of times interest is charged in a year
t is the number of years
The principal amount is 1000 dollars, while the rate of interest is 6.75% which is compounded monthly. Therefore, the time it will need for the account to reach $2500 is,
2500 = 1000[1+(0.0675/12)¹²ˣⁿ
2.5 = (1.0675)¹²ⁿ
log(2.5)\ log(1.0675) = 12n
14.0278 = 12n
n = 1.1689 ≈ 1.2
Hence, the time for which the person must leave the money in the bank until it reaches $2500 is 1.2.
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Answer: 13.6 years
Step-by-step explanation: Dealta Math Answer
Which graph represents the following system of inequalities?
y>2x-5
y<-3x
give an answer with graph
The graph of the two given system of inequalities y > 2x - 5
y < -3x is; Attached below
How to graph Inequalities?We are given two inequalities;
y > 2x - 5
y < -3x
The graph that represents the 2 inequalities has been attached and from the graph, we see that;
The slope of the dotted line is negativeThe x- intercept of the dotted line is the point (0,0)The y- intercept of the dotted line is the point (0,0)The solution of the system of inequalities is the shaded pink area between the two dotted lines.
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HELP ASAP PLEASE
Sabrina grows flowers. In a
competition with other flower growers,
she earned the following scores: 7, 10, 10, 6, 7, 8, 8, 7, 9.
a. What is the median?
b. What is the first quartile?
c. What is the third quartile?
d. Draw a box plot of the data.
e. Write two conclusions about the data shown in the box plot.
Answer:
a. median is 8
b. first quartile is 7
c. third quartile is 9.5
d. below
e. below
Step-by-step explanation:
7, 10, 10, 6, 7, 8, 8, 7, 9.
Place number in order least to greatest
6, 7, 7, 7, 8, 8, 9, 10, 10
a. What is the median?
The median is the middle number in a data set
number of terms in data set (n) + 1 / 2 =
9 + 1 / 2 = 10 / 2
6, 7, 7, 7, 8, 8, 9, 10, 10
The median is 8
b. What is the first quartile?
Q1 is the central point between the smallest score and the median
6, 7, 7, 7
since there is even number of data points you find the average,
7 + 7 / 2 = 14 / 2 = 7
c. What is the third quartile?
Q3 is the central point between the median and the largest score
8, 9, 10, 10
since there is even number of data points you find the average,
9 + 10 / 2 = 19 / 2 = 9.5
d. Draw a box plot of the data.
below
e. Write two conclusions about the data shown in the box plot.
There are no outliers with a minimum of 6 and a maximum of 10. The Interquartile Range is 2.5 (9.5 - 7)
X^2-4x+6=0 solve by completing square
Complete the square:
x² - 4x + 6 = 0
x² - 4x = -6
x² - 4x + 4 = -6 + 4
(x - 2)² = -2
But the left side is positive for any real number x, so there are no real solutions.
If you're solving over the complex numbers, we can go on to say
x - 2 = ± √(-2)
x - 2 = ± 2i
x = 2 ± 2i
where i = √(-1).
the spec sheet for the actual 1968 corvette shows the front frame dimension to be 32.875 inches. what would this measurement be, in both fractional and decimal form, on the hot wheels 1:64 model? which form of the measurement would be easier to work with?
Answer:
0.513671875 = 263/512 inches
easier to use: depends on the measurement tool
Step-by-step explanation:
The model dimension is found by multiplying the actual dimension by the scale factor.
__
model dimensionmodel frame dimension = actual frame dimension × 1/64
= (32.875 inches)/64 = 0.513671875 inches
In fractional form, this is ...
(32 7/8) / 64 = (263/8) / 64 = 263/512 . . . inches
__
ease of useIt is unlikely that a casual hobbyist will have access to tools that measure with a resolution finer than 0.0001 inches. More common would be a measurement resolution of 0.001 inches. Using such tools, the rounded decimal value 0.5137 or 0.514 inches would be more useful than the fractional measurement.
It is possible that an optical measuring device could be available that would present its result as a fraction of an inch. If such a tool were used, the fractional measurement value would provide an appropriate point of comparison.
In short, the measurement easiest to work with depends on the tool being used to make the measurement.
Directions: Solve the following by multiplying by the inverse of the fractional coefficient. 1. \frac{2}{5} t = 20 2. \frac{7}{8} p = 56 3. \frac{5}{6} x = 30 4. \frac{1}{2} x = 20 5. \frac{3}{5} s = 60 6. \frac{1}{3} t = 3 7. \frac{3}{4} x = 9 8. \frac{11}{12} x = 11 9. \frac{8}{10} t = 80 10. \frac{p}{3} = 9 11. \frac{n}{5} = 30 12. \frac{6a}{7} = 36 13. \frac{1}{2} t + 3 = 28 14. \frac{1}{6} r = 12 15. \frac{11}{12} b = 32
The answer of the following options are as 50, 64, 36, 40, 100, 9, 12, 12 100, 27, 150 42, 50 72, 28.3.
How to interpret the fraction?Suppose the fraction is proper (the numerator is smaller than the denominator).
Let it be
[tex]\dfrac{a}{b}[/tex]
Then, we can interpret it as:
a parts out of b parts of a thing.
[tex]1. \dfrac{2}{5} t = 20\\\\t = 20 \times \dfrac{5}{2}\\\\t= 50[/tex]
[tex]2. \frac{7}{8} p = 56\\\\p = 56 \times \frac{8}{7} \\\\ p= 64[/tex]
[tex]3. \frac{5}{6} x = 30 \\\\x = 30 \times \frac{6}{5} = 36[/tex]
[tex]4. \frac{1}{2} x = 20\\\\x = 20 \times 2 = 40[/tex]
[tex]5. \frac{3}{5} s = 60\\\\s = 60 \times \frac{5}{3} = 100[/tex]
[tex]6. \frac{1}{3} t = 3 \\\\t = 3\times 3 = 9[/tex]
[tex]7. \frac{3}{4} x = 9\\\\x = 12[/tex]
[tex]8. \frac{11}{12} x = 11\\\\x = 11 \times 12/11 = 12[/tex]
[tex]9. \frac{8}{10} t = 80\\\\t = 80 \times 10/8 = 100[/tex]
[tex]10. \frac{p}{3} = 9 \\\\p = 9 \times 3 = 27[/tex]
[tex]11. \frac{n}{5} = 30\\\\n = 30 \times 5 = 150[/tex]
[tex]12. \frac{6a}{7} = 36 \\\\a = 36 \times 7/6 = 42[/tex]
[tex]13. \frac{1}{2} t + 3 = 28\\\\t = (28 - 3)2 = 50[/tex]
[tex]14. \frac{1}{6} r = 12\\\\r = 12\times 6 = 72[/tex]
[tex]15. \frac{11}{12} b = 32\\ \\b = 32 \times 11/12 = 29.33[/tex]
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Help me out, please!
Answer:
a = 63
b = 117
c = 63
Step-by-step explanation:
The sum of interior angles in a triangle is = 180
so the measure of a:
85 + 32 + a = 180 add like terms
117 + a = 180 subtract 117 from both sides
a = 63
a and be are supplementary angles so their sum is equal to 180
180 - 63 = 117 is the b's value
since a and c are on a pair of parallel lines, their value must be equal therefore the value of c is also 63
Find the area of the trapezoid.
The image is of a trapezoid with the lengths of lower and upper parallel sides marked as 12 in. and 8 in. respectively. The length of left side of the trapezoid which is perpendicular to the base is 7 in. and the fourth side is 8 in.
A. 140 in.2
B. 35 in.2
C. 75 in.2
D. 70 in.2
Answer:
Its a for me
Step-by-step explanation:
trust me fuys
Which expression is equivalent in to the given expression? Assume the denominator does not equal zero.
14r4y6
718y2
OA 2y4
OB. 7y3
OC. 7r4y4
OD. 2x²y³
The equivalent expression of 14r^4y^6/7r^8y^2 is 2y^4/r^4
How to determine the equivalent function?The expression is given as:
14r^4y^6/7r^8y^2
Start by dividing 14 by 7
2r^4y^6/r^8y^2
Next divide y^6 by y^2
2r^4y^4/r^8
Lastly divide r^4 by r^8
2y^4/r^4
Hence, the equivalent expression of 14r^4y^6/7r^8y^2 is 2y^4/r^4
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Mary throws a plastic disc to her friend. Her friend
catches the disc six seconds after Mary throws it. The
table shows the height of the disc at one-second
intervals.
Time (seconds)
Height (feet)
0
3
1
A
2
6
3
7
6
4
B
4
5
6
Mark this and return
Assuming that the throw represents projectile motion,
what are the missing values in the table?
O A = 5, B = 3
O A=4, B=0
O A=4, B = 3
O A = 5, B = 0
Submit
Next
By assuming that the motion of the plastic disc thrown by Mary is a projectile motion, the missing values are 4 and 3 respectively.
How to determine the missing height?Since we're assuming that the motion of the plastic disc thrown by Mary is a projectile motion, it simply means that the motion can be represented by a quadratic function (parabolic).
For a projectile motion, the height of the disc at the time when it's at the top would be the same (equal). Thus, we can logically deduce that:
Height at time (t = 1 seconds) = Height at time (t = 5 seconds)
4 = A.
Similarly, Height at time (t = 0 seconds) = Height at time (t = 6 seconds)
3 = B.
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The CEO of a company wants to determine if taking the employees to a company retreat would boost their morale. He decides to use a random number table to survey a simple random sample of 50 of the 250 employees. Which of the following correctly labels the population of employees?
000-250
001-250
0-250
1-250
Answer:
1-250 i think
Answer: B
Step-by-step explanation:
trust me bro
The methods of solving quadratic equations
There are three main ways of solving quadratic equations. The quadratic formula, factoring, and completing the square.
[1] using the quadratic formula
When the equation is in the form of ax² + bx + c = 0.
[tex]\displaystyle x=\frac{-b\pm\sqrt{b^2-4ac} }{2a}[/tex]
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[2] factoring
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[3] completing the square
To start out with completing the square, make sure your constant is isolated on one side. The equation will be as ax² + bx = -c
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12.simplify the following expression
21q + 5/2(3/2) + 4q -5
Answer:
i think the answer is 25q - 5 / 4
If 56 pr+6:54 Pr+3 = 30800: 1, find the value of r.
Answer:
Sorry po Hindi ko po alm :(
Serenity earned a grade of 39% on her multiple choice science final that had a total of
200 problems. How many problems on the final exam did Serenity answer correctly?
Answer:
78
Step-by-step explanation:
The number of correct problems is found by multiplying the percentage that were correct by the total number of problems.
__
number correct = fraction correct × number of problems
number correct = 0.39 × 200 = 78
Serenity answered 78 problems correctly.
_____
Additional comment
The symbol % is fully equivalent to /100. That is 39% = 39/100 = 0.39 (pronounced "thirty-nine hundredths"). Using a percent symbol is just another way to write a fraction.
Consider the function.
Which conclusions can be drawn about f–1(x)? Select two options.
f–1(x) has a slope of .
f–1(x) has a restricted domain.
f–1(x) has a y-intercept of (0, –36).
f–1(x) has an x-intercept of (–36, 0).
f–1(x) has a range of all real numbers.
The statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
What is a function?
It is defined as a special type of relationship, and they have a predefined domain and range according to the function every value in the domain is related to exactly one value in the range.
The question is incomplete.
The question is: Consider the function f(x) = (-2/3)x - 24 Which conclusions can be drawn about f⁻¹(x) Select two options:
f⁻¹(x) has a slope of -2/3
f⁻¹(x) has a restricted domain.
f⁻¹(x) has a y-intercept of (0, –36).
f⁻¹(x) has an x-intercept of (–36, 0).
f⁻¹(x) has a range of all real numbers.
f(x) = (-2/3)x - 24
To find the inverse of a function:
interchange the x and y
x = (-2/3)y - 24
y = (-3/2)(x + 24)
y = (-3/2)x - 36
The slope of a function f⁻¹(x) is -3/2
From the graph, we can see the y-intercept is (0, -36) and the range will be all real numbers.
Thus, the statement f⁻¹(x) has a y-intercept of (0, –36) and f⁻¹(x) has a range of all real numbers options third and fifth are correct.
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Answer:
D and E
Step-by-step explanation:
did the test
G(F(x)) = 7√√x+1
A. F(x)=√x and G(x) = 7
B. F(x)= x and G(x) = √√7
C. F(x) = 7x and G(x)=√x+1
D. F(x)=√x+1 and G(x) = 7x
Answer:
D)
Step-by-step explanation:
[tex]\sf f(x) = \sqrt{x+1}\\\\\\g(x) = 7x\\\\ g(f(x)) = g(\sqrt{x+1}) = 7*\sqrt{x+1}[/tex]
A candle on Pauline’s dresser is 4 inches tall and burns at a rate of 0.6 inches per hour. How many hours will it take for the candle to burn down to a height of 1.3 inches?
The time taken for the candle to burn down to a height of 1.3 inches is 4.5 hours
What is a Linear Function ?A linear function is what can be written in the form of
y =mx+c
The rate at which the candle is burning is 0.6 inches/ hour
The initial height is 4 inches at t=0
The straight line equation can be written for this as
y =mx +c
as m = -0.6
at x = 0 , y = 4 therefore c =4
y = -0.6x +4
The time at which y = 1.3 inches is
1.3 = -0.6x +4
-2.7 = -0.6 x
x =4.5
4.5 hours is the time taken for the candle to burn down to a height of 1.3 inches.
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One block is needed to make an up-down-up staircase with one step up and one step down.
Four blocks are need to build and up-down-up staircase with 2 steps up and 2 steps down.
Complete parts (a) and (b) below.
***
a. How many blocks are needed to build an up-down-up staircase with 5 steps up and 5 steps down?
25 blocks are needed to build an up-down-up staircase with 5 steps up and 5 steps down.
(Type a whole number.)
b. How many blocks are needed to build an up-down-up staircase with n steps up and n steps down?
blocks are needed to build an up-down-up staircase with n steps up and n steps down.
Answer:
n² blocks are needed to build a staircase with n steps.
Step-by-step explanation:
what are the soltuions to the quadratic equation below? 12x squared + 4x -5=0
Answer: 0.5 or - 0.834
Step-by-step explanation: Here is the explanation!
Can someone help it’s a little confusing
Orange traffic cones comes in a variety of sizes. Approximate the volume, in cubic inches, of a traffic cone
that has a height of 2 feet and a diameter of 16 inches. Round your answer to the nearest tenth. Use 3.14
for a.
Answer:
V = 1607.7 in^3
V = 0.94 ft^3
Step-by-step explanation:
To find the volume of a traffic cone, use the formula for the volume of a cone: (1/3)*π*h*r^2
h = height
r = radius of cone
Step 1: determine variables and units
2 feet = 24 inches
diameter = 2 * radius
radius = (1/2) * diameter = (1/2)*16 in = 8 inches
Step 2: determine volume
V = (1/3)*π*h*r^2
V = (1/3)*3.14*24*(8)^2
V = 1607.7 in^3
Optional step 3: determine volume in ft^3
h = 2 ft
r = 0.67 ft
V = (1/3)*π*h*r^2 = (1/3)*3.14*2*(0.67)^2
V = 0.94 ft^3
Michael spent $700 in April and May and $800 in June and July. His average monthly expenses are:
His average monthly expenses are: $750
How to determine the average monthly expenses?The given parameters are:
April and May = $700June and July = $800The average monthly expenses are calculated using:
Average = Total expenses/Number of months
So, we have:
Average = (700 + 700 + 800 + 800)/4
Evaluate
Average = 750
Hence, his average monthly expenses are: $750
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At the beginning of the month, a rain barrel contained 12 ounces of water. At the end of the month there are 814 cups of water in the rain barrel.
How many cups of rain water were added to the barrel during the month?
Enter your answer as a mixed number in simplest form by filling in the boxes.
Upon searching for your question, I believe there are 8 [tex]\frac{1}{4}[/tex] cups, and not 814 cups.
Answer: 6 [tex]\frac{3}{4}[/tex] cups of water
Step-by-step explanation:
First, we will turn 12 ounces into units of cups.
12 / 8 = 1.5 cups
Now, we will subtract the start of the month from the end of the month.
8.25 cups - 1.5 cups = 6.75 cups
Lastly, we will turn it into a mixed number.
.75 = [tex]\frac{3}{4}[/tex]
6 [tex]\frac{3}{4}[/tex] cups
6 [tex]\frac{3}{4}[/tex] cups of water were added to the barrel during the month.
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Pls need helppp in this question
Show all work. Find the measure of <1. Show all work.
Its in the picture below.
The value of x is 7 and the measure of ∠1 is 99
How to solve for x?The given parameters are:
∠NMQ = 5x + 19∠MQN = 8x - 11∠QNM = 11x + 4The sum of angles in a triangle is 180.
So, we have:
5x + 19 + 8x - 11 + 11x + 4 = 180
Evaluate the like terms
24x = 168
Divide both sides by 24
x = 7
Hence, the value of x is 7
How to determine the measure of ∠1?The angles on a straight line add up to 180.
This means that:
∠1 + ∠QNM = 180
Subtract ∠QNM from both sides
∠1 = 180 - ∠QNM
Substitute ∠QNM = 11x + 4
∠1 = 180 - 11x - 4
Substitute x = 7
∠1 = 180 - 11 * 7- 4
Evaluate
∠1 = 99
Hence, the measure of ∠1 is 99
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Find the value of x of the given right triangle.
Answer:
In the right triangle, the side a=[tex]4[/tex] and the hypotenuse c=[tex]7[/tex].
To find: the value of x
We have,
[tex]a=6[/tex] and [tex]c=7[/tex]
Now,by the pythagorean theorem,
[tex] {a}^{2} + {b}^{2} = {c}^{2} [/tex]
Substitute the values,
[tex] {6}^{2} + {x}^{2} = {7}^{2} [/tex]
[tex]36 + {x}^{2} = 49[/tex]
Subtract 36 from each sides,
[tex] {x}^{2} = 13[/tex]
Take square root from each sides,
[tex]x = \sqrt{13} [/tex]
Hence, the value of x is [tex]\sqrt{13}[/tex].
Consider the sets A = {4,6,8} and B = {4,5,6} Find Ax B (b) Find the power set AB)
a) A × B is the Cartesian product of A and B, given by the set
A × B = {(a, b) | a ∈ A and b ∈ B}
Then for A = {4, 6, 8} and {4, 5, 6}, we have the product
A × B = {(4, 4), (4, 5), (4, 6), (6, 4), (6, 5), (6, 6), (8, 4), (8, 5), (8, 6)}
b) The power set of a set X is the set containing all subsets of X. I'm not sure what you're asking to find the power set of, though. Hopefully it's not of A × B, since that would contain 2⁹ = 512 elements...
Instead I'll assume you mean a simpler set, such as A ∩ B. The intersection of A and B is
A ∩ B = {4, 6, 8} ∩ {4, 5, 6} = {4, 6}
and has only 2 elements, so its power set has 2² = 4 elements (much more manageable!) and is the set
Pow(A ∩ B) = {{}, {4}, {6}, {4, 6}}